Air France argues that it needs to cut costs to stay competitive in the face of tough rivalry from budget airlines and Gulf state carriers. Pilots are protesting plans to shift some activities to low-cost carrier Transavia and shift some jobs to countries with lower taxes and labor costs.

Government spokesman Stephane le Foll said Wednesday that the strike should stop and urged a return to negotiations. The French state owns 15.9 percent of Air France.

Air France planes sit on the tarmac at Paris-Charles de Gaulle airport in Roissy, on Sept. 17, 2014.

ERIC FEFERBERG/AFP/Getty Images

Air France is running only about 40 percent of its flights worldwide Wednesday, day three of the strike.

The strike is also affecting American passenger - a look at random U.S.-France flights operated by the airline showed that a number were canceled on Wednesday. Cities with cancellations include New York, Los Angeles and Chicago. The airline asks passengers to visit its website for flight status updates.